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Block #72,875

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 2:40:47 AM Β· Difficulty 8.9944 Β· 6,743,347 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
eca36a9e8b05a9c187b5215a493639c05eda01e1a38a8b75cb335c554adbc0ef
View on Chainz β†—

Height

#72,875

Difficulty

8.994407

Transactions

1

Size

204 B

Version

2

Bits

08fe9178

Nonce

875

Timestamp

7/21/2013, 2:40:47 AM

Confirmations

6,743,347

Merkle Root

930e484ffafe973d78ca2c474bea51cb143a639958d8a8a388275040aeee7c76
Transactions (1)
Coinbase930e484ffafe97…275040aeee7c76
1 in β†’ 1 out12.3400 XPM110 B
APxUMipn…2zpbPwcA
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.664 Γ— 10¹⁰⁡(106-digit number)
16642265596283359747…73976752540635066880
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.664 Γ— 10¹⁰⁡(106-digit number)
16642265596283359747…73976752540635066881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.328 Γ— 10¹⁰⁡(106-digit number)
33284531192566719494…47953505081270133761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.656 Γ— 10¹⁰⁡(106-digit number)
66569062385133438989…95907010162540267521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.331 Γ— 10¹⁰⁢(107-digit number)
13313812477026687797…91814020325080535041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.662 Γ— 10¹⁰⁢(107-digit number)
26627624954053375595…83628040650161070081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.325 Γ— 10¹⁰⁢(107-digit number)
53255249908106751191…67256081300322140161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.065 Γ— 10¹⁰⁷(108-digit number)
10651049981621350238…34512162600644280321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.130 Γ— 10¹⁰⁷(108-digit number)
21302099963242700476…69024325201288560641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 72875

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock eca36a9e8b05a9c187b5215a493639c05eda01e1a38a8b75cb335c554adbc0ef

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #72,875 on Chainz β†—
Circulating Supply:57,773,904 XPMΒ·at block #6,816,221 Β· updates every 60s
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